Behavioral optimal consumption and portfolio selection in continuous time

Thesis

This thesis mainly concerns a continuous-time behavioral consumption model under Kahneman and Tversky’s cumulative prospect theory. Mathematically this is a non- concave maximization problem because of the presence of an S-shaped functional and the presence of so-called probability distortions. By using a quantile method and divide-and-conquer scheme, we solve the problem quite explicitly and the optimal consumption is in general characterized in two parts: the agent has rich consumption above the benchmark in good situations and suffers from hunger (i.e. no consumption) in bad situations. An example is given to show that judging whether the market is good or bad depends highly on the agent’s benchmark. Finally we give the strategy for optimal consumption and portfolio selection to maximize behavioral utilities from both consumption and terminal wealth.

Authors: Wang, K

• Publication date: 2013
• Type of award: MSc by Research
• Level of award: Masters
• Awarding institution: Oxford University, UK
• Language: English
• Keywords: divide-and-conquer; consumption; quantile method; cumulative prospect theory
• Subjects: Mathematics; Mathematical finance